Problem: Solve for $x$ and $y$ using elimination. ${x+5y = 23}$ ${-x-2y = -11}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x+5y = 23}\thinspace$ to find $x$ ${x + 5}{(4)}{= 23}$ $x+20 = 23$ $x+20{-20} = 23{-20}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {-x-2y = -11}\thinspace$ and get the same answer for $x$ : ${-x - 2}{(4)}{= -11}$ ${x = 3}$